A shop sells one-pound bags of peanuts for $2 and three-pound bags of peanuts for $5.
If 9 bags are purchased for a total cost of $36, how many three-pound bags were
purchased?
the answer is 9
Let's solve this problem step by step.
Step 1: Assign variables.
Let's assign variables to represent the unknown quantities.
Let's say:
P = number of one-pound bags purchased
T = number of three-pound bags purchased
Step 2: Set up an equation for the total cost.
The cost of one-pound bags is $2, and the cost of three-pound bags is $5. The total cost of 9 bags is $36.
So we can write the equation:
2P + 5T = 36
Step 3: Set up a second equation for the total number of bags.
The total number of bags purchased is 9.
So we can write the equation:
P + T = 9
Step 4: Solve the system of equations.
We have two equations with two variables. We can solve this system of equations using substitution or elimination.
Let's use the substitution method:
From equation 3, we can isolate P as follows:
P= 9 - T
Substitute this value for P in equation 2:
2(9 - T) + 5T = 36
Simplify the equation:
18 - 2T + 5T = 36
3T = 36 - 18
3T = 18
T = 18 / 3
T = 6
Step 5: Find the value of P.
Now substitute the value of T into equation 3:
P = 9 - T
P = 9 - 6
P = 3
Step 6: Answer the question.
According to the solution, 3 three-pound bags were purchased.
Therefore, 3 three-pound bags were purchased.
To solve this problem, let's assign variables to the unknown quantities. Let's say the number of one-pound bags purchased is represented by x, and the number of three-pound bags purchased is represented by y.
Given that one-pound bags cost $2 and three-pound bags cost $5, we can create equations based on the given information.
First, we know that the total cost of all the bags purchased is $36. This can be expressed as:
2x + 5y = 36
We also know that the total number of bags purchased is 9. This can be expressed as:
x + y = 9
To solve these equations, we can use a method called substitution. We can solve one equation for one variable and then substitute that value into the other equation.
Let's solve the second equation for x:
x = 9 - y
Now, we can substitute this value of x into the first equation:
2(9 - y) + 5y = 36
18 - 2y + 5y = 36
3y = 36 - 18
3y = 18
y = 6
Therefore, 6 three-pound bags were purchased.
O + T = 9
T = 9 - O
2O + 5T = 36
Substitute 9-O for T in last equation and solve for O. Insert that value into the first equation and solve for T. Check by inserting both values into the second equation.